History of Logic Timeline

Christian philosophers such as Boethius (died 524), through translations and commentaries, preserved and transmitted Aristotle's logic to the medieval West, shaping scholastic philosophy for centuries.

Image source: Boethius

Until the twelfth century, the only works of Aristotle available in the West were the Categories, On Interpretation, and Boethius's translation of the Isagoge of Porphyry (a commentary on the Categories).

An important work in the medieval logical tradition was the Logica Ingredientibus of Peter Abelard (1079–1142), which made significant contributions to the theory of universals and semantics.

Image source: Peter Abelard

The proof for the principle of explosion, also known as the principle of Pseudo-Scotus, according to which any proposition can be proven from a contradiction, was first given by the 12th century French logician William of Soissons.

By the early thirteenth century, the remaining works of Aristotle's Organon, including the Prior Analytics, Posterior Analytics, and the Sophistical Refutations (collectively known as the Logica Nova or 'New Logic'), had been recovered in the West.

Image source: Organon

Christian philosophers such as Thomas Aquinas (died 1274) further developed Aristotle's logic in the Middle Ages, incorporating it deeply into theology and natural philosophy.

Image source: Thomas Aquinas

William of Ockham (died 1347) further developed Aristotle's logic in the Middle Ages, contributing influential work on supposition theory and terminism within scholastic logic.

Image source: William of Ockham

Christian and Islamic philosophers further developed Aristotle's logic in the Middle Ages, reaching a high point in the mid-fourteenth century with Jean Buridan, whose work on sophismata and consequences marked the peak of scholastic logic.

Image source: Jean Buridan

Ibn Sina (Avicenna) (980–1037) was the founder of Avicennian logic, which replaced Aristotelian logic as the dominant system of logic in the Islamic world, and also had an important influence on Western medieval writers such as Albertus Magnus.

Image source: Avicenna

Al-Ghazali (1058–1111, died 1111; his influential critique appeared by 1149 in later works' reception) criticised Aristotle's 'first figure' and formulated an early system of inductive logic, foreshadowing the system of inductive logic developed by John Stuart Mill (1806–1873).

Image source: Al-Ghazali

The Illuminationist school was founded by Shahab al-Din Suhrawardi (1155–1191), who developed the idea of 'decisive necessity', referring to the reduction of all modalities (necessity, possibility, contingency and impossibility) to the single mode of necessity.

Maimonides (1138-1204) wrote a Treatise on Logic (Arabic: Maqala Fi-Sinat Al-Mantiq), referring to Al-Farabi as the 'second master', the first being Aristotle.

Image source: Maimonides

Fakhr al-Din al-Razi (1149–1249) developed a form of logic revolving around the subject matter of conceptions and assents, influencing later Islamic logical thought.

In response to the Post-Avicennian school, Nasir al-Din al-Tusi (1201–1274) began a tradition of Neo-Avicennian logic which remained faithful to Avicenna's work and existed as an alternative to the more dominant Post-Avicennian school over the following centuries.

Image source: Nasir al-Din al-Tusi

Ibn al-Nafis (1213–1288) wrote a book on Avicennian logic, which was a commentary of Avicenna's Al-Isharat (The Signs) and Al-Hidayah (The Guidance).

Image source: Ibn al-Nafis

The period between the fourteenth century and the beginning of the nineteenth century saw largely decline and neglect, and at least one historian of logic regards this time as barren, though thousands of pages on logic were still written, especially in the Islamic world.

The last great works in the scholastic tradition are the Logic of John Poinsot (1589–1644, known as John of St Thomas), the Metaphysical Disputations of Francisco Suarez (1548–1617), and the Logica Demonstrativa of Giovanni Girolamo Saccheri (1667–1733).

Image source: John of St. Thomas

Empirical methods ruled the day, as evidenced by Sir Francis Bacon's Novum Organon of 1620, an influential work proposing induction as the foundation of scientific reasoning.

Image source: Novum Organum

Published in 1662, the Port-Royal Logic was the most influential work on logic after Aristotle until the nineteenth century. Between 1664 and 1700, there were eight editions, and the book had considerable influence after that.

Image source: Port-Royal Logic

Other works in the textbook tradition include Isaac Watts's Logick: Or, the Right Use of Reason (1725), Richard Whately's Logic (1826), and John Stuart Mill's A System of Logic (1843), which treated logic largely as a descriptive science.

Image source: A System of Logic

Hegel indicated the importance of logic to his philosophical system when he condensed his extensive Science of Logic into a shorter work published in 1817 as the first volume of his Encyclopaedia of the Philosophical Sciences.

Image source: Science of Logic

Logic revived in the mid-nineteenth century, at the beginning of a revolutionary period when the subject developed into a rigorous and formal discipline which took as its exemplar the exact method of proof used in mathematics, a hearkening back to the Greek tradition.

Carl von Prantl's Geschichte der Logik im Abendland (1855–1867) provided a major historical survey of Western logic, reflecting renewed scholarly interest in the discipline during its revival period.

Image source: Karl von Prantl

Bradley's Principles of Logic (1883) was an important idealist contribution to logic during the era when logic was widely treated as a descriptive science and branch of psychology.

Image source: F. H. Bradley

Gergonne said that reasoning does not have to be about objects about which one has perfectly clear ideas, because algebraic operations can be carried out without having any idea of the meaning of the symbols involved — an early anticipation of symbolic logic.

Image source: Joseph Diez Gergonne

The algebraic school begins with Boole's seminal work Mathematical Analysis of Logic which appeared in 1847, although De Morgan (1847) is its immediate precursor. The success of Boole's algebraic system suggested that all logic must be capable of algebraic representation.

Image source: George Boole

Jevons published Pure Logic, or the Logic of Quality apart from Quantity in 1864, where he suggested a symbol to signify exclusive or, which allowed Boole's system to be greatly simplified.

Image source: William Stanley Jevons

Boole's early work lacked the idea of the logical sum which originates in Peirce (1867), Schröder (1877) and Jevons (1890), and the concept of inclusion, first suggested by Gergonne (1816) and clearly articulated by Peirce (1870).

Image source: Charles Sanders Peirce

In 1869 Jevons realised that Boole's methods could be mechanised, and constructed a 'logical machine' which he showed to the Royal Society the following year. In 1885 Allan Marquand proposed an electrical version of the machine that is still extant.

Image source: Logical machine

In his Symbolic Logic (1881), John Venn used diagrams of overlapping areas to express Boolean relations between classes or truth-conditions of propositions, creating what are now known as Venn diagrams.

Image source: John Venn

Schröder's monumental Vorlesungen über die Algebra der Logik ('Lectures on the Algebra of Logic', vol iii 1895) ambitiously expressed a logic of relations in algebraic form. He set out theorems in parallel columns in this work (1890–1905).

Image source: Ernst Schröder (mathematician)

Between the work of Mill and Frege, logic was widely treated as a descriptive science, essentially a branch of psychology. It was subjected to an extended and destructive critique by Edmund Husserl in the first volume of his Logical Investigations (1900), an assault described as 'overwhelming'.

The logicist project received a near-fatal setback with the discovery of a paradox in 1901 by Bertrand Russell, showing that naive set theory leads to contradiction.

Image source: Russell's paradox

The monumental Principia Mathematica, a three-volume work on the foundations of mathematics, written by Russell and Alfred North Whitehead and published 1910–1913 included an attempt to resolve the paradox by means of an elaborate system of types: one cannot speak of the 'set of all sets'.

Image source: Principia Mathematica

The metamathematical period from 1910 to the 1930s saw the development of metalogic, in the finitist system of Hilbert, and the non-finitist systems of Löwenheim and Skolem, culminating in the combination of logic and metalogic in the work of Gödel and Tarski.

Image source: Metamathematics

Peirce (1880) showed how all Boolean elective functions could be expressed using a single primitive binary operation, 'neither...nor...', but like many of Peirce's innovations, this remained unknown until Sheffer rediscovered it in 1913.

Work on metamathematics culminated in the work of Gödel, who in 1929 showed that a given first-order sentence is deducible if and only if it is logically valid, establishing the completeness of first-order predicate logic.

Image source: Gödel's completeness theorem

Gödel's incompleteness theorem of 1931 was one of the greatest achievements in the history of logic, showing that any consistent formal system capable of arithmetic contains true statements that cannot be proved within the system.

In 1933, Tarski published (in Polish) The concept of truth in formalized languages, in which he proposed his semantic theory of truth: a sentence such as 'snow is white' is true if and only if snow is white. According to Anita Feferman, Tarski 'changed the face of logic in the twentieth century'.

Alonzo Church and Alan Turing proposed formal models of computability, giving independent negative solutions to Hilbert's Entscheidungsproblem in 1936 and 1937 respectively, founding theoretical computer science.

Progress in mathematical logic in the first few decades of the twentieth century, particularly arising from the work of Gödel and Tarski, had a significant impact on analytic philosophy and philosophical logic, particularly from the 1950s onwards, in subjects such as modal logic, temporal logic, deontic logic, and relevance logic.

Paul Cohen introduced forcing in 1963 to prove the independence of the continuum hypothesis and the axiom of choice from Zermelo–Fraenkel set theory, earning him the Fields Medal.

Image source: Forcing (mathematics)

Another logical system founded after World War II was fuzzy logic by Azerbaijani mathematician Lotfi Asker Zadeh in 1965, allowing reasoning with degrees of truth rather than strict true/false values.

Image source: Fuzzy logic

Saul Kripke's best known and most influential work is Naming and Necessity (1980), which reshaped analytic philosophy of language and revitalized modal logic.

Image source: Naming and Necessity